Ray's New Practical Arithmetic · Arts. 164–165 · Unit 14: Percentage

77. Finding the percentage and finding the rate

Goal: Your child finds a per cent of a number (Case I) and finds what per cent one number is of another (Case II).

⏱ About 35 minutes · 6 steps

Open it at the Internet Archive ↗

You'll need

  • Paper and pencil, or a slate or small whiteboard

What's in the book

Page 199 gives Case I (Art. 164) with two worked examples, the rule and problems 3–16. Page 200 has more Case I problems and Case II (Art. 165) with two worked examples, and page 201 the Case II problems. Answers are printed.

The lesson, step by step

  1. Warm-up

    Ask: What is 10% of 50? 50% of 30? 25% of 80?

  2. Case I

    Given the base and the rate, to find the percentage.

    What is 25% of 32?

    25% is 1/4, and 1/4 of 32 is 8.

    What is 7% of 162?

    .07 × 162 = 11.34.

    Multiply the base by the rate; the product will be the percentage.

    The book adds that you may use a fraction or a decimal, whichever is simpler.

  3. Case II

    Given the base and the percentage, to find the rate.

    What per cent of 8 is 2?

    2 is 1/4 of 8, and 1/4 is 25%.

    What per cent of 56 is 3.5?

    3.5 ÷ 56 = .0625 = 6¼%.

    SayDivide the part by the whole.

  4. Guided practice

    Do these together:

    What per cent of 15 is 3?

    What per cent of 9 is 13.5?

    The second is more than 100%. Talk about why.

  5. Independent practice and check

    Your child works a selection of the Case I problems (pages 199–200) and the Case II problems (page 201). The book prints the answer at the end of each problem line. Have your child cover the answers with a strip of paper, work the problem, then slide the strip down to check.

  6. Mental-math wrap-up

    Aloud: 1% of 278; 10% of 57; what per cent of 50 is 25? what per cent of 4 is 1?

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