Ratios and Rate Reasoning: math test solutions, Grade 6 – download the PDF

1 Describing a garden / 3 pts

(a) \( 12:18 = 2:3 \) (1 pt)

(b) There are \( 12 + 18 + 6 = 36 \) flowers, so \( 6:36 = 1:6 \). (1 pt)

(c) \( 18:12 = 3:2 \). (1 pt)

2 Equivalent ratios / 3 pts

(a) \( 5 \times 4 = 20 \), so \( 8 \times 4 = 32 \). (1 pt)

(b) \( 8 \times 7 = 56 \), so \( 5 \times 7 = 35 \). (1 pt)

(c) Yes: \( 12:20 = 3:5 \) (divide by 4) and \( 21:35 = 3:5 \) (divide by 7). (1 pt)

3 Cereal prices / 4 pts

(a) Brand X: \( 4.50 \div 18 = 0.25 \) dollar per ounce (1 pt). Brand Y: \( 6.90 \div 30 = 0.23 \) dollar per ounce (1 pt).

(b) \( 0.23 < 0.25 \), so Brand Y is the better buy. (1 pt)

(c) \( 90 = 30 \times 3 \), so the cost is \( 3 \times 6.90 = 20.70 \) dollars. (1 pt)

4 Jogging speed / 3 pts

(a) 60 minutes is \( 20 \times 3 \), so she jogs \( 2.5 \times 3 = 7.5 \) miles in an hour: 7.5 miles per hour. (2 pts)

(b) \( 50 \div 20 = 2.5 \), so the distance is \( 2.5 \times 2.5 = 6.25 \) miles. (1 pt)

5 Beads / 4 pts

Draw 4 boxes for red and 3 boxes for yellow. (1 pt)

There are \( 4 + 3 = 7 \) boxes. (1 pt)

One box is \( 63 \div 7 = 9 \) beads. (1 pt)

Red: \( 4 \times 9 = 36 \) beads. Yellow: \( 3 \times 9 = 27 \) beads. Check: \( 36 + 27 = 63 \). (1 pt)

6 Printing job / 3 pts

(a) \( 45 \div 6 = 7.5 \) pages per minute. (1 pt)

(b) \( 150 \div 7.5 = 20 \). (1 pt)

It takes 20 minutes. (1 pt)