Adding and Subtracting Fractions Worksheets

Tanya takes half an hour to reach the dance class. She practices dance for

\frac{1}{4}

of an hour in the morning and

\frac{1}{3}

of an hour in the evening. What is the time spent on dance practice?

	a.		$\frac{7}{12}$ of an hour
	b.		$\frac{2}{3}$ of an hour
	c.		$\frac{1}{12}$ of an hour
	d.		$\frac{3}{5}$ of an hour

Solution:

Time spent on dance practice = 1 / 4 + 1 / 3
[Time spent in the morning + Time spent in the evening]

= 3 / 12 + 4 / 12
[Write equivalent fractions using the LCD, 12.]

= 7 / 12
[Since the denominators are same, add the numerators.]

Tanya spent 7 / 12 of an hour on dance practice.

At a bakery, each cake was cut into 8 equal pieces. Andrew sold 5 pieces of a cake, Amy sold 4 pieces of another, and Sarah sold 7 pieces of another. Which expression can be used to find the total number of cakes sold by these 3 people?

	a.		$\frac{8}{5}$ + $\frac{8}{4}$ + $\frac{8}{7}$
	b.		1 - $\frac{7}{8}$ - $\frac{5}{8}$ - $\frac{4}{8}$
	c.		$\frac{5}{8}$ + $\frac{4}{8}$ + $\frac{7}{8}$
	d.		1 + $\frac{5}{8}$ + $\frac{4}{8}$ + $\frac{7}{8}$

Solution:

Andrew sold 58 of a cake.

Amy sold 48 of a cake.

Sarah sold 78 of a cake.

So, the expression that represents the total number of cakes sold by these 3 people = 58 + 48 + 78.

Steve bought

2 \frac{3}{5}

pounds of grapes,

1 \frac{2}{5}

pounds of nuts, and

3 \frac{4}{5}

pounds of apples. Which expression can be used to find the total weight of all the three items that Steve bought?

	a.		2 $\frac{3}{5}$ + 1 $\frac{2}{5}$ + 3 $\frac{4}{5}$
	b.		2 $\frac{3}{5}$ + 1 $\frac{2}{5}$
	c.		1 + 2 $\frac{3}{5}$ + 1 $\frac{2}{5}$ + 3 $\frac{4}{5}$
	d.		1 - 2 $\frac{3}{5}$ + 1 $\frac{2}{5}$ + 3 $\frac{4}{5}$

Solution:

Steve bought 23 / 5 pounds of grapes, 12 / 5 pounds of nuts, and 34 / 5 pounds of apples.

So, the expression that can be used to find the total weight of all the three items that Steve bought = 235 + 125 + 345.

Tim ate

\frac{3}{5}

of a pie. Sunny ate

\frac{1}{5}

of a pie. Carlos ate

1 \frac{2}{10}

pies. Which expression can be used to find the total number of pies consumed by these 3 boys?

	a.		1 - $\frac{3}{5}$ + $\frac{1}{5}$ + 1 $\frac{2}{10}$
	b.		$\frac{3}{5}$ + $\frac{1}{5}$ + 1 $\frac{2}{10}$
	c.		$\frac{3}{5}$ + $\frac{1}{5}$ + $\frac{2}{10}$
	d.		1 + $\frac{3}{5}$ + $\frac{1}{5}$ + 1 $\frac{2}{10}$

Solution:

Tim ate 3 / 5 of a pie.

Sunny ate 1 / 5 of a pie.

Carlos ate 12 / 10 pies.

So, the expression that represents the total number of pies consumed by these 3 boys = 35 + 15 + 1210.

Which statement leads you through to estimate mentally the quotient of

\frac{117}{50}

to the nearest tenth?
I. Use a calculator.
II. Check for numbers that multiply with 50 to give 117.
III. The fraction is easily convertible to a fraction with a denominator of 100.

	a.		III
	b.		I and II
	c.		II
	d.		I

Solution:

Statement I is ruled out, as we need to estimate the quotient mentally.

Statement II is about trial and error method. You keep trying different numbers until you find the relevant one, and sometimes you may not find one.

As suggested in statement III, we shall convert the fraction 11750 into 234100 just by multiplying its numerator and denominator by 2.

234100 = 2.34 ≈ 2.3, to the nearest tenth.

Among the statements given, statement III would lead us through the estimation.

Estimate using compatible numbers the sum of

\frac{64}{21}

and

\frac{55}{112}

to the nearest tenth.

	a.		3.0
	b.		3.5
	c.		4.5
	d.		4.0

Solution:

6421 ≈ 6321 = 3
[64 is close to 63 and is compatible with 21.]

55112 ≈ 55110 = 1 / 2 = 0.5
[112 is close to 110 and is compatible with 55.]

So, 6421 + 55112 ≈ 3 + 0.5 = 3.5 to the nearest tenth.

Annie had a board

2 \frac{1}{3}

ft long. She bought another board

1 \frac{1}{5}

ft long and attached it to the first one. Estimate the total length of the board.

	a.		6 ft
	b.		3 ft
	c.		2 ft
	d.		5 ft

Solution:

Length of the board initally = 21 / 3 ft

21 / 3 = 2 + 1 / 3 ≈ 2 + 0 = 2
[1 / 3 = 0.33333. . . ≈ 0.]

Length of the board attached = 11 / 5

11 / 5 = 1 + 1 / 5 ≈ 1 + 0 = 1
[1 / 5 = 0.2 ≈ 0.]

Therefore, the total length of the board = 21 / 3 + 11 / 5 ≈ 2 + 1 = 3 ft

A container holds

10 \frac{1}{9}

pints of liquid. If

\frac{1}{5}

of it is juice, estimate the quantity of juice in the container.

	a.		4 pints
	b.		6 pints
	c.		8 pints
	d.		2 pints

Solution:

Quantity of liquid container holds = 101 / 9

1019 = 10 + 19 ≈ 10 + 0 = 10
[1 / 9 = 0.111111. . . ≈ 0.]

Quantity of juice in the container ≈ 1 / 5 × 10 = 2 pints

Quantity of juice in the container is 2 pints.

Andrew bought a cake. He gave

\frac{1}{4}

of it to his brother,

\frac{1}{6}

of it to his sister, and

\frac{1}{2}

of it to his friend. What fraction of the cake did he distribute?

	a.		$\frac{7}{12}$
	b.		$\frac{1}{12}$
	c.		$\frac{5}{12}$
	d.		$\frac{11}{12}$

Solution:

The fraction of cake Andrew distributed = Fraction of cake he gave to his brother + Fraction of cake he gave to his sister + Fraction of cake he gave to his friend

= 1 / 4 + 1 / 6 + 1 / 2

= 3 + 2 + 612 = 1112
[Take LCD and add.]

The fraction of cake he distributed is 11 / 12.

10.

Lauren ate

\frac{1}{5}

of a pizza and Zelma ate

\frac{1}{4}

of it. Which operation would help you to find the fraction of pizza that Lauren and Zelma ate in all?

	a.		addition
	b.		division
	c.		multiplication
	d.		subtraction

Solution:

Fraction of pizza that Lauren and Zelma ate = Fraction of pizza that Lauren ate + Fraction of pizza that Zelma ate

The fraction of pizza that Lauren and Zelma ate is found using the operation additon.

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