Question

name:
date:
period:
4 - 9. find the missing parts of each number line. assume that the lines have been split into equal parts. homework help

a.

b.

c.

Explanation:

Part a

Step1: Determine number of parts

The number line from 0 to 42 is split into 6 equal parts (since there are 6 intervals between 0 and 42). We need to find the length of 2 parts (from the first mark after 0 to the third mark, so 2 intervals? Wait, looking at the diagram, the question mark is over 2 segments? Wait, no, let's count the divisions. From 0 to 42, there are 6 marks (including 0 and 42), so 5 intervals? Wait, no, the diagram shows 0, then 5 marks, then 42. Wait, maybe 6 equal parts. Let's calculate the length of one part: total length is 42, number of parts is 6 (since from 0 to 42, there are 6 segments? Wait, the diagram has 0, then a mark, then another, up to 42. Let's see: 0 to 42, divided into 6 equal parts. So each part is \( \frac{42}{6} = 7 \). Then the missing part is 2 parts? Wait, the question mark is over 2 segments? Wait, looking at the diagram, the first segment after 0, then the next, so 2 segments? Wait, no, maybe 2 parts. Wait, if total parts are 6, then each part is 7. Then the missing length is 2 parts: \( 2 \times 7 = 14 \). Wait, maybe I miscounted. Let's check again. The number line from 0 to 42: how many intervals? Let's see, the marks are at 0, then 6 marks, then 42? Wait, the diagram shows 0, then a vertical line, then 5 more vertical lines, then 42. So total intervals: 6. So each interval is \( 42 \div 6 = 7 \). The question mark is over 2 intervals (from the first mark after 0 to the third mark? Wait, no, the first interval is 0 to first mark, second to second, etc. Wait, the question mark is over 2 intervals. So \( 2 \times 7 = 14 \).

Step2: Calculate missing length

Total length: 42, number of parts: 6. Length per part: \( \frac{42}{6} = 7 \). Number of parts in missing section: 2. So missing length: \( 2 \times 7 = 14 \).

Step1: Determine number of parts

The number line from 0 to 64 is split into 8 equal parts (since there are 8 intervals? Wait, the diagram shows 0, then 7 marks, then 64. So 8 intervals. Each part length: \( \frac{64}{8} = 8 \). The missing part is 4 parts (from the second mark to the sixth mark, so 4 intervals). Wait, the question mark is over 4 segments? Let's check: 0 to 64, 8 parts. Each part is 8. So 4 parts: \( 4 \times 8 = 32 \).

Step2: Calculate missing length

Total length: 64, number of parts: 8. Length per part: \( \frac{64}{8} = 8 \). Number of parts in missing section: 4. So missing length: \( 4 \times 8 = 32 \).

Step1: Determine number of parts

The number line from 0 to 24 is split into 6 equal parts (since there are 6 intervals? Wait, the diagram shows 0, then 5 marks, then 24. So total intervals: 6. Each part length: \( \frac{24}{6} = 4 \). The question mark is over 4 parts (from the first mark after 0 to the fifth mark? Wait, no, the question mark is over 4 intervals. Let's see: 0 to 24, 6 intervals. Each interval is 4. The missing length is 4 intervals: \( 4 \times 4 = 16 \). Wait, let's confirm: total length 24, 6 parts, so each part 4. Missing section is 4 parts: \( 4 \times 4 = 16 \).

Step2: Calculate missing length

Total length: 24, number of parts: 6. Length per part: \( \frac{24}{6} = 4 \). Number of parts in missing section: 4. So missing length: \( 4 \times 4 = 16 \).

Answer:

14

Part b