# Estimating Fractions Worksheet

Estimating Fractions Worksheet
• Page 1
1.
Estimate:
1,636 ÷ 38
 a. 100 b. 30 c. 60 d. 41

#### Solution:

We can use compatible numbers to estimate the quotient.

38 40 and 1636 1640, a number divisible by 40.

1636 ÷ 38 1640 ÷ 40 = 41

2.
Which statement leads you through to estimate mentally the quotient of $\frac{191}{25}$ to the nearest tenth?

I. The fraction is easily convertible to a fraction with a denominator of 100.

II. Look for numbers that multiply with 25 to give 191.

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

#### Solution:

As suggested in statement I, we shall convert the fraction 19125 into 764100 just by multiplying its numerator and denominator by 4.

764100 = 7.64 7.6
[Round down 7.64 to the nearest tenths.]

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

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

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

3.
Estimate, using compatible numbers, the sum of $\frac{46}{22}$ and $\frac{35}{71}$ to the nearest tenth.
 a. 2.5 b. 2 c. 3 d. 2.3

#### Solution:

4622 4422 = 2
[46 is close to 44 and is compatible with 22.]

3571 3570 = 1 / 2 = 0.5
[70 is close to 71 and is compatible with 35.]

4622 + 3571 2 + 0.5 = 2.5 to the nearest tenths.

4.
Alice bought a sack of potatoes that weighs $\frac{1}{9}$ lb and a sack of tomatoes that weighs $\frac{7}{8}$ lb. Estimate the total weight of the vegetables.
 a. $1\frac{3}{8}$ lb b. $3\frac{1}{2}$ lb c. 4 lb d. 1 lb

#### Solution:

19 0
[1 / 9 is close to 0.]

78 1
[7 / 8 is close to 1.]

Estimated total weight of the vegetables = 0 + 1 = 1 lb

5.
A can holds $12\frac{4}{9}$ quarts of liquid. If $\frac{1}{3}$ of it is water, estimate the quantity of water in the can.
 a. 4 quarts b. 8 quarts c. 12 quarts d. 3 quarts

#### Solution:

Total quantity of liquid the can holds = 124 / 9 12 quarts.

The estimated quantity of water in the can = 12 × 1 / 3 = 4 quarts.

6.
Estimate the product of $\frac{19}{6}$ and 11.
 a. 33 b. 114 c. 66 d. 22

#### Solution:

196 3

3 × 11 = 33

So, the approximate product of 19 / 6 and 11 is 33.

7.
$4\frac{3}{4}$ ${cm}^{3}$ of wood is required to make one box. Estimate the wood required for making 5 boxes.
 a. 60 ${cm}^{3}$ b. 5 ${cm}^{3}$ c. 25 ${cm}^{3}$ d. 75 ${cm}^{3}$

#### Solution:

434 5

Approximately 5 cm3 of wood is required to make 1 box.

Wood required for making 5 boxes = 5 × 5 = 25 cm3

So, approximately 25 cm3 of wood is required for making 5 boxes.

8.
A whale gains a weight of $8\frac{1}{3}$ lb in $4\frac{1}{3}$ months. Estimate the weight gained by the whale in one month.
 a. 2 lb b. 18 lb c. 4 lb d. 12 lb

#### Solution:

81 / 3 8 and 41 / 3 4

81 / 3 ÷ 41 / 3 = 8 ÷ 4 = 2

So, the approximate weight gained by the whale in one month is 2 lb.

9.
Estimate the quotient of 12.125 divided by 0.8112.
 a. 12 b. 8 c. 18 d. 15

#### Solution:

Round 12.125 to 12 and 0.8112 to 0.8.
[Estimating the quotient of two decimals is to round both the divisor and dividend to one non-zero digit, and then divide the rounded decimals.]

12 ÷ 0.8 = 15

So, the estimated quotient of 12.125 divided by 0.8112 is 15.

Cost of 3 m of a wire is $14.87. Estimate the cost of 8.17 m of the wire.  a.$40 b. $66 c.$72 d. $36 #### Solution:$14.87 $15 Cost of 3 m of wire$15.
So, cost of 1 m of wire $5. 8.17 m 8 m Cost of 8 m of wire 5 × 8 =$40