☰ خطة العام · الرياضيات (بالإنجليزية)

Ratios with tape diagrams and number lines

الأسبوع 19 · النسب بأشرطة القياس وخطوط الأعداد والمقارنة · 3 دروس
2

Equivalent ratios on a double number line

Discover Mathematics P6: Term 2, Unit 9, Lessons 4–6
GoalUse a double number line or a table to find missing values by scaling.
New words
double number line · two number lines, one for each quantity, matched value by valuescale up · to multiply both terms by the same numberscale down · to divide both terms by the same number
Explanation

A double number line has two lines, one above the other. Both start at 0. Each mark on the top line is matched with a mark on the bottom line, and the pairs are equivalent ratios. For rice and water in the ratio 2 : 3, the top line goes 0, 2, 4, 6, 8, 10 and the bottom line goes 0, 3, 6, 9, 12, 15. To find a missing value, scale: ask what you multiply or divide by to go from the known value to the value you need, then do the same to the other term. A table (a ratio table) holds the same information.

★Remember
Same step on both lines. Multiply or divide both terms by the same number. Both lines start at 0.
Worked examples
double number line
Rice (cups)0246810
Water (cups)03691215
Rice and water are in the ratio 2 : 3. The double number line shows the matching amounts. So 10 cups of rice need 15 cups of water (× 5), and 6 cups of water go with 4 cups of rice.
Blue (cans)3691215
White (cans)510152025
A paint mix uses 3 cans of blue for every 5 cans of white. The table gives 3 : 5, 6 : 10, 9 : 15, 12 : 20, 15 : 25. So 12 cans of blue go with 20 cans of white, and 15 cans of white go with 9 cans of blue.
Missing value by dividing. 12 : 20 = 3 : ?. Going from 12 to 3 we divide by 4, so we also divide 20 by 4 and get 5. Therefore 12 : 20 = 3 : 5.
Class activity

Double line on paper. Draw two parallel lines on a strip of paper. Choose a ratio from a recipe at home and mark five equivalent pairs. Use it to answer two questions that nobody can answer by looking only at the first pair.

Practice
1
Complete the ratio table for 3 : 7 up to 4 columns.
2
Rice and water are in the ratio 2 : 3. How much rice goes with 21 cups of water?
3
A mixture has 1 cup of sugar for every 4 cups of flour. How much flour for 3 cups of sugar?
4
Find the missing number: 5 : 8 = 20 : ?
5
Find the missing number: 6 : 9 = ? : 3