Informative line

# Word Problems on Decimals

In real life, we need to do calculations quite frequently.

In our daily life, there are countless examples of arithmetic problems as to calculate the daily expenditure, to find increment and decrement in temperature etc.

So, in order to solve real life problems, we need to identify what kind of operations are to be performed.

In order to figure out, which operation is to be applied in a given word problem, following logics can be used.

• Addition : If the values of more than one units are given and the problem asks to determine the total units, then addition is used to calculate the total units.
• Subtraction : If the values of two or more units are given and problem asks for the difference of units, then subtraction is used to calculate the difference.
• Multiplication : If the value of a single unit is given and the problem asks for the values of more than one units, then multiplication is used.
• Division : If the values of more than one units are given and the problem asks for the value of a single (each) unit, then division is to be performed.

For example : Four girls went to a restaurant and spent $$$50.50$$ in total. They split the bill evenly among them selves. How much did each girl pay? Number of girls = $$4$$ Total amount spent on dinner =$$$50.50$$

To calculate how much did each girl pay, we will divide $$50.50$$ by $$4$$.

$$50.50÷4=12.625$$

Hence, each girl pays $$$12.625$$ #### Illustration Questions #### Sam earns$$$8.25$$ per hour for his work. If he works $$6$$ hours/day, how much money does he earn in a day?

A $$$49.5$$ B$$$14.25$$

C $$$2.25$$ D$$$10$$

×

The amount Sam earns per hour = $$$8.25$$ Number of hours for which Sam works = $$6$$ hours/day To calculate how much amount Sam earns in a day, we multiply $$8.25$$ by $$6$$. So, total amount = $$8.25 ×6 = 49.5$$ Thus, Sam will earn$$$49.5$$

Hence, option (A) is correct.

### Sam earns $$$8.25$$ per hour for his work. If he works $$6$$ hours/day, how much money does he earn in a day? A$$$49.5$$

.

B

$$$14.25$$ C$$$2.25$$

D

\$$$10$$

Option A is Correct

In real life, we need to do calculations quite frequently.

In our daily life, there are countless examples of arithmetic problems as to calculate the daily expenditure, to find increment and decrement in temperature etc.

So, in order to solve real life problems, we need to identify what kind of operations are to be performed.

For example: Alex buys a DVD player for $$49.95$$ and a DVD holder for $$19.95$$. If he pays $$100$$, how much money does he get back?

Cost of a DVD player = $$49.95$$

Cost of a DVD holder = $$19.95$$

To calculate the total cost of the items, we will add the costs of both the items.

$$\Rightarrow \;49.95+19.95=69.9$$

To calculate the amount he gets back, we will subtract the total cost of items from the amount he paid.

$$\Rightarrow \100-69.9=30.1$$

Thus, Alex gets $$30.1$$ back.

#### Ms. Wendy thought of buying $$1.5$$ pounds of snacks but could buy only $$0.75$$ pounds of peanuts and $$0.35$$ pounds of raisins. How many pounds of snacks could she not buy?

A 1.1 Pounds

B 0.5 Pounds

C 0.4 Pounds

D 0.1 Pounds

×

Quantity of peanuts bought by Ms. Wendy = $$0.75$$ pounds

Quantity of raisins bought by Ms. Wendy = $$0.35$$ pounds

To calculate total quantity of snacks, we will add the amounts of both the snacks

$$\Rightarrow\;0.75+0.35=1.1$$ pounds

But, Ms. Wendy thought of buying $$1.5$$ pounds of snacks.

To calculate the amount of snacks that she could not buy, we will subtract $$1.1$$ from $$1.5$$

$$\Rightarrow1.5-1.1=0.4$$ Pounds

So, Ms. Wendy could not buy $$0.4$$ pounds of snacks.

Hence, option (C) is correct.

### Ms. Wendy thought of buying $$1.5$$ pounds of snacks but could buy only $$0.75$$ pounds of peanuts and $$0.35$$ pounds of raisins. How many pounds of snacks could she not buy?

A

1.1 Pounds

.

B

0.5 Pounds

C

0.4 Pounds

D

0.1 Pounds

Option C is Correct

# Subtraction and Multiplication

In real life, we need to do calculations quite frequently.

In our daily life, there are countless examples of arithmetic problems as to calculate the daily expenditure, to find increment and decrement in temperature etc.

So, in order to solve real life problems, we need to identify what kind of operations are to be performed.

For example :

Daniel wants to buy some posters which cost $$9.99$$ each but are offered on sale at $$2.35$$ less. If he buys $$5$$ posters, how much he spends?

To calculate the sale price of one poster, we will subtract $$2.35$$ from $$9.99$$,

$$9.99-2.35=7.64$$

Sale price of one poster is $$7.64$$

To calculate the cost of $$5$$ posters, we will multiply $$7.64$$ by $$5$$,

$$7.64×5=38.2$$

Thus, Daniel spends $$38.2$$

#### Carlos needs to buy $$6$$ pens and some colored pencils for sketching. He has $$20.00$$ to spend. If the cost of one pen is $$2.25$$ and he buys $$6$$ pens. How much amount he is left with to buy colored pencils?

A $$17.75$$

B $$6.50$$

C $$22.25$$

D $$8.25$$

×

Cost of a single pen = $$2.25$$

To calculate the total cost of $$6$$ pens,

we will multiply $$2.25$$ by $$6$$,

$$=2.25×6=13.5$$

Total cost of $$6$$ pens is $$13.5$$

To calculate how much money he is left with to buy colored pencils, we will subtract $$13.5$$ from $$20.00$$,

$$20.00-13.50=6.50$$

So, Carlos has $$6.50$$ to spend on colored pencils.

Hence, option (B) is correct.

### Carlos needs to buy $$6$$ pens and some colored pencils for sketching. He has $$20.00$$ to spend. If the cost of one pen is $$2.25$$ and he buys $$6$$ pens. How much amount he is left with to buy colored pencils?

A

$$17.75$$

.

B

$$6.50$$

C

$$22.25$$

D

$$8.25$$

Option B is Correct

In real life, we need to do calculations quite frequently.

In our daily life, there are countless examples of arithmetic problems as to calculate the daily expenditure, to find increment and decrement in temperature etc.

So, in order to solve real life problems, we need to identify what kind of operations are to be performed.

For example :

Ms. Wendy made $$30.25$$ in the first week and $$41.65$$ in the second week by snow shoveling. She decided to divide the total amount equally among her two little sisters. How much amount did each sister get?

To calculate the total amount made by Ms. Wendy, we will add $$30.25$$ and $$41.65$$,

$$30.25+41.65=71.90$$

Ms. Wendy divided $$71.90$$ equally among her two sisters.

To calculate, how much money each sister got, we will divide $$71.90$$ by $$2$$.

$$71.90÷2=35.95$$

Hence, each sister got $$35.95$$

#### Toby, Miles, Emma and Jane planned a backyard picnic. They bought $$0.5\,\ell$$ lemonade bottle and four cups of the same capacity. The lemonade was not sufficient for the four, so they poured the lemonade in the bigger jar and mixed $$0.5\,\ell$$ water to it. How much of the mix did each one get?

A $$0.5\,\ell$$

B $$0.25\,\ell$$

C $$10\,\ell$$

D $$1.5\,\ell$$

×

Quantity of Lemonade $$=0.5\,\ell$$

Quantity of water = $$0.5\,\ell$$

Total quantity of mix $$=0.5+0.5=1\,\ell$$

Number of persons $$=4$$

$$\therefore$$ Quantity of mix to each person $$=1\,\ell÷4=0.25\,\ell$$

Hence, option (B) is correct.

### Toby, Miles, Emma and Jane planned a backyard picnic. They bought $$0.5\,\ell$$ lemonade bottle and four cups of the same capacity. The lemonade was not sufficient for the four, so they poured the lemonade in the bigger jar and mixed $$0.5\,\ell$$ water to it. How much of the mix did each one get?

A

$$0.5\,\ell$$

.

B

$$0.25\,\ell$$

C

$$10\,\ell$$

D

$$1.5\,\ell$$

Option B is Correct

In real life, we need to do calculations quite frequently.

In our daily life, there are countless examples of arithmetic problems as to calculate the daily expenditure, to find increment and decrement in temperature etc.

So, in order to solve real life problems, we need to identify what kind of operations are to be performed.

For example :

In Cooper's shopping cart, he has $$3$$ pounds of oranges at $$0.95$$ per pound, $$4$$ cans of soup at $$1.21$$ per can, and $$2$$ cups of ice cream at $$1.1$$ per cup. What is the total cost of the items in his shopping cart?

To calculate the total cost of each item, we multiply the number of items by the cost of each item.

Total cost of 3 pounds of oranges:

$$3×0.95=2.85$$

Total cost of 4 cans of soup:

$$4×1.21=4.84$$

Total cost of 2 cups of ice cream:

$$2×1.1=2.2$$

To calculate the total cost of all items in his shopping cart, we will add the total cost of the three items.

$$\Rightarrow2.85+4.84+2.2=9.89$$

So, Cooper has items worth $$9.89$$ in his shopping cart.

#### Three friends went to watch a movie show. The cost of each ticket was $$8$$. They bought soda and popcorn bags for each one of them. The costs of 1 soda and 1 popcorn bag were $$1.75$$ and $$2.25$$ respectively. Calculate the total amount spent by them.

A $$4.25$$

B $$10$$

C $$36$$

D $$12.25$$

×

The number of friends = $$3$$

To calculate the total cost of each item, we will multiply the cost of each item by $$3$$,

Total cost of 3 tickets:

$$3×8=24$$

Cost of 3 sodas:

$$3×1.75=5.25$$

Cost of 3 bags of popcorn:

$$3×2.25=6.75$$

To calculate the total amount spent by them, we will add the costs of all the items,

$$\Rightarrow24+5.25+6.75=36$$

Hence, option (C) is correct.

### Three friends went to watch a movie show. The cost of each ticket was $$8$$. They bought soda and popcorn bags for each one of them. The costs of 1 soda and 1 popcorn bag were $$1.75$$ and $$2.25$$ respectively. Calculate the total amount spent by them.

A

$$4.25$$

.

B

$$10$$

C

$$36$$

D

$$12.25$$

Option C is Correct

# Subtraction and Multiplication

In real life, we need to do calculations quite frequently.

In our daily life, there are countless examples of arithmetic problems as to calculate the daily expenditure, to find increment and decrement in temperature etc.

So, in order to solve real life problems, we need to identify what kind of operations are to be performed.

For example:

Emma sold $$5$$ hats at $$22.8$$ each. She used all the money to buy $$8$$ pairs of socks. What was the price of each pair of socks?

To calculate the total cost of $$5$$ hats, we will multiply $$22.8$$ by $$5$$,

$$22.8×5=114$$

She sold $$5$$ hats for $$114$$.

To calculate the price of each pair of socks, we will divide $$114$$ by $$8$$,
$$114÷8=14.25$$

Thus, cost of each pair of socks was $$14.25$$

#### Alex makes a target to walk $$11.2$$ miles in $$7$$ days & he can walk $$1$$ mile in $$1.2$$ hours. How much time he should walk each day?

A $$1.92$$ hours

B $$2.32$$ hours

C $$4$$ hours

D $$1$$ hour

×

To calculate the total hours of walking, we will multiply $$11.2$$ with $$1.2$$,

$$=11.2×1.2=13.44$$ hours

He takes $$13.44$$ hours in total to complete his target.

To calculate the time of walk for each day, we will divide $$13.44$$ by $$7$$,

$$=13.44÷7=1.92$$ hours (Converting $$92$$ minutes in hours)

$$=2.32$$ hours

Thus, Alex should walk for $$2.32$$ hours each day.

Hence, option (B) is correct.

### Alex makes a target to walk $$11.2$$ miles in $$7$$ days & he can walk $$1$$ mile in $$1.2$$ hours. How much time he should walk each day?

A

$$1.92$$ hours

.

B

$$2.32$$ hours

C

$$4$$ hours

D

$$1$$ hour

Option B is Correct

# Subtraction and Division

In real life, we need to do calculations quite frequently.

In our daily life, there are countless examples of arithmetic problems as to calculate the daily expenditure, to find increment and decrement in temperature etc.

So, in order to solve real life problems, we need to identify what kind of operations are to be performed.

For example :

Kelly spent a total of $$15.00$$ on an evening, of which $$9.8$$ were spent on movie show tickets and with the rest amount she bought $$2$$ drinks. If each drink had the same cost, how much did each drink cost?

To calculate the total amount spent on drinks, we will subtract $$9.8$$ from $$15.00$$,

$$15.00-9.80=5.20$$

So, she spent $$5.20$$ on 2 drinks.

To calculate the cost of each drink, we will divide $$5.2$$ by $$2$$,

$$5.2÷2=2.6$$

Thus, each drink costs $$2.6$$

#### The area of a circle is $$1.6\,\pi\,cm^2$$. If a quarter part is removed from it, what will be the area of the remaining part?

A $$1.0\,\pi\,cm^2$$

B $$1.2\,\pi\,cm^2$$

C $$0.6\,\pi\,cm^2$$

D $$1.5\,\pi\,cm^2$$

×

Area of the given circle $$=1.6\,\pi\,cm^2$$

Area of quarter part of the circle

$$=1.6\,\pi\,÷4$$

$$=0.4\,\pi\,cm^2$$

Area of the remaining portion = Area of Circle – Area of quarter part

$$=1.6\,\pi\,-0.4\,\pi$$

$$=1.2\,\pi\,cm^2$$

Hence, option (B) is correct.

### The area of a circle is $$1.6\,\pi\,cm^2$$. If a quarter part is removed from it, what will be the area of the remaining part?

A

$$1.0\,\pi\,cm^2$$

.

B

$$1.2\,\pi\,cm^2$$

C

$$0.6\,\pi\,cm^2$$

D

$$1.5\,\pi\,cm^2$$

Option B is Correct