USING BENCHMARKS AND PROPORTIONAL REASONING

We can use certain benchmark percents to write other percents and to estimate fractions.

Let us consider the picture given below.

From the above picture, we can consider the following benchmark percents.

1/10 = 10%

1/3 = 33⅓%

1/2 = 50%

2/3 = 66⅔%

3/4 = 75%

Solved Questions

Question 1 :

Find an equivalent percent for 3/10.

Answer :

Step 1 :

Write 3/10 as a multiple of a benchmark fraction.

That is,

3/10 = 3 x 1/10

(Think : 3/10 = 1/10 + 1/10 + 1/10)

Step 2 :

Find an equivalent percent for 1/10.

Use the number lines to find the equivalent percent for 1/10.

1/10 = 10%

Step 3 :

Multiply.

3/10 = 3 x 1/10

3/10 = 3 x 10%

3/10 = 30%

Question 2 :

76% of the students at a middle school bring their own lunch. About what fraction of the students bring their own lunch?

Answer :

Step 1 :

Note that 76% is close to the benchmark 75%.

Step 2 :

Find a fraction equivalent for 75%.

That is,

75% = 75/100 = 3/4

About 3/4 of the students bring their own lunch.

Question 3 :

Use a benchmark to find an equivalent percent for the fraction 9/10.

Answer :

Step 1 :

Write 9/10 as a multiple of a benchmark fraction.

That is,

9/10 = 9 x 1/10

Step 2 :

Find an equivalent percent for 1/10.

Use the number lines to find the equivalent percent for 1/10.

1/10 = 10%

Step 3 :

Multiply.

9/10 = 9 x 1/10

9/10 = 9 x 10%

9/10 = 90%

Question 4 :

Use a benchmark to find an equivalent percent for the fraction 2/5.

Answer :

Step 1 :

Write 2/5 as a multiple of a benchmark fraction.

That is,

2/5 = (2x2)/(5x2)

2/5 = 4/10

2/5 = 4 x 1/10

Step 2 :

Find an equivalent percent for 1/10.

Use the number lines to find the equivalent percent for 1/10.

1/10 = 10%

Step 3 :

Multiply.

4/10 = 4 x 1/10

4/10 = 4 x 10%

4/10 = 40%

Question 5 :

64% of the animals at an animal shelter are dogs. About what fraction of the animals at the shelter are dogs?

Answer :

Step 1 :

Note that 64% is close to the benchmark 66⅔%.

Step 2 :

Find a fraction equivalent for 66⅔%.

That is,

66⅔% = 2/3

About 2/3 of the animals at the shelter are dogs.

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