Learn to use a table to find equivalent ratios and rates.

Reading Math Finding equivalent ratios is sometimes referred to as “scaling up” or “scaling down.”

Use a table to find ratios equivalent to 3 to 2. Original Ratio 3 • 2 3 • 3 3 • 4 8 6 4 2 Pints of blue 12 9 3 Pints of yellow 2 • 2 2 • 3 2 • 4 You can increase amounts but keep them in the same ratio by multiplying both the numerator and denominator of the ratio by the same number. The ratios 3 to 2, 6 to 4, 9 to 6, and 12 to 8 are equivalent. You can also decrease amounts in the same ratio by dividing the numerator and denominator by the same number.

Additional Example 1A: Making a Table to Find Equivalent Ratios Use a table to find the equivalent ratios. 6 7 __ Original Ratio 6 • 2 6 • 3 6 • 4 Multiply the numerator and the denominator by 2, 3, and 4. 7 6 12 18 24 14 21 28 7 • 2 7 • 3 7 • 4 6 7 __ 12 14 ___ 18 21 ___ 24 28 ___ The ratios , , , and are equivalent.

Helpful Hint Multiplying by 2, 3, and 4 will give you three equivalent ratios, but there are many other equivalent ratios that are correct.

Additional Example 1B: Making a Table to Find Equivalent Ratios Use a table to find the equivalent ratios. 3 to 5 Original Ratio 3 • 2 3 • 3 3 • 4 Multiply the numerator and the denominator by 2, 3, and 4. 5 3 6 9 12 10 15 20 5 • 2 5 • 3 5 • 4 The ratios 3 to 5, 6 to 10, 9 to 15, and 12 to 20 are equivalent.

Additional Example 1C: Making a Table to Find Equivalent Ratios Use a table to find the equivalent ratios. 48:36 Original Ratio 48 ÷ 2 48 ÷ 3 48 ÷ 4 Divide the numerator and the denominator by 2, 3, and 4. 36 48 24 16 12 18 12 9 36 ÷ 2 36 ÷ 3 36 ÷ 4 The ratios 48:36, 24:18, 16:12, and 12:9 are equivalent.

Use a table to find the equivalent ratios. Check It Out: Example 1A Use a table to find the equivalent ratios. 3 8 __ Original Ratio 3 • 2 3 • 3 3 • 4 Multiply the numerator and the denominator by 2, 3, and 4. 8 3 6 9 12 16 24 32 8 • 2 8 • 3 8 • 4 3 8 __ 6 16 ___ 9 24 ___ 12 32 ___ The ratios , , , and are equivalent.

Use a table to find the equivalent ratios. 2 to 9 Check It Out: Example 1B Use a table to find the equivalent ratios. 2 to 9 Original Ratio 2 • 2 2 • 3 2 • 4 Multiply the numerator and the denominator by 2, 3, and 4. 9 2 4 6 8 18 27 36 9 • 2 9 • 3 9 • 4 The ratios 2 to 9, 4 to 18, 6 to 27, and 8 to 36 are equivalent.

Use a table to find the equivalent ratios. 36:12 Check It Out: Example 1C Use a table to find the equivalent ratios. 36:12 Original Ratio 36 ÷ 2 36 ÷ 3 36 ÷ 4 Divide the numerator and the denominator by 2, 3, and 4. 12 36 18 12 9 6 4 3 12 ÷ 2 12 ÷ 3 12 ÷ 4 The ratios 36:12, 18:6, 12:4, and 9:3 are equivalent.

Additional Example 2: Application Several groups of friends are going to take a shuttle bus to the park. The table shows how much the different groups will pay in all. Predict how much a group of 15 friends will pay. 36 24 12 Bus Fare($)‏ 18 6 Number in Group 12< 15 < 18; therefore, the group will pay between $24 and $36.

Additional Example 2 Continued 36 24 12 Bus Fare($)‏ 18 6 Number in Group Use the amount paid by the group of 6. Divide the bus fare by the number in each group to find the amount paid per person. 12 ÷ 6 = 2 2 • 15 = 30 Multiply. A group of 15 friends will pay $30 in bus fare.

Check It Out: Example 2 Several groups of friends are purchasing tickets to an amusement park. The table shows how much the different groups will pay in all. Predict how much a group of 7 friends will pay. 40 30 20 Tickets($)‏ 8 6 4 Number in Group 6 < 7 < 8; therefore, the group will pay between $30 and $40.

Check It Out: Example 2 Continued 40 30 20 Tickets($)‏ 8 6 4 Number in Group Use the amount paid by the group of 8. Divide the ticket prices by the number of people in each group to find the amount paid per person. 40 ÷ 8 = 5 5 • 7 = 35 Multiply. A group of 7 friends will pay $35 for amusement park tickets.