Question

name
practice
write a decimal that names the same point on the number line.

1. \\(\frac{1}{2}\\)
2. \\(1\frac{1}{5}\\)
3. \\(1\frac{2}{5}\\)
4. \\(\frac{10}{10}\\)
5. \\(\frac{3}{5}\\)
6. \\(1\frac{3}{10}\\)
7. \\(\frac{7}{10}\\)
8. \\(\frac{0}{10}\\)

write the letter that shows each fraction, mixed number, or decimal.

1. \\(\frac{2}{2}\\)
2. \\(1\frac{4}{8}\\)
3. \\(1\frac{2}{8}\\)
4. \\(\frac{6}{3}\\)
5. 1.75
6. \\(\frac{1}{4}\\)
7. 0.75
8. \\(\frac{6}{12}\\)

circle the fraction or mixed number that is equivalent to the decimal.

1. 0.2 \\(\frac{1}{5}\\) \\(\frac{1}{2}\\) \\(\frac{2}{10}\\)
2. 0.4 \\(\frac{1}{4}\\) \\(\frac{2}{5}\\) \\(\frac{6}{10}\\)
3. 1.4 \\(1\frac{1}{4}\\) \\(1\frac{2}{5}\\) \\(1\frac{14}{10}\\)
4. 0.9 \\(\frac{1}{9}\\) \\(\frac{9}{1}\\) \\(\frac{9}{10}\\)
5. 0.8 \\(\frac{1}{8}\\) \\(\frac{8}{10}\\) \\(\frac{10}{8}\\)
6. 2.1 \\(\frac{2}{1}\\) \\(2\frac{1}{10}\\) \\(2\frac{21}{10}\\)
7. 1.2 \\(1\frac{1}{2}\\) \\(1\frac{1}{5}\\) \\(1\frac{2}{12}\\)
8. 0 \\(\frac{0}{1}\\) \\(\frac{1}{1}\\) \\(\frac{1}{10}\\)
9. 4.5 \\(4\frac{5}{1}\\) \\(4\frac{5}{10}\\) \\(\frac{45}{10}\\)

math reasoning number sense

1. write the letter that shows where \\(2\frac{3}{4}\\) is located on this number line.

explain how you decided.
chapter 14 - lesson 4

Explanation:

Step1: Solve Question 1

To convert \(\frac{1}{2}\) to a decimal, divide 1 by 2. \(1\div2 = 0.5\).

Step2: Solve Question 2

First, convert the mixed number \(1\frac{1}{5}\) to an improper fraction: \(1\frac{1}{5}=\frac{6}{5}\). Then divide 6 by 5: \(6\div5 = 1.2\).

Step3: Solve Question 3

Convert \(1\frac{2}{5}\) to an improper fraction: \(1\frac{2}{5}=\frac{7}{5}\). Divide 7 by 5: \(7\div5 = 1.4\).

Step4: Solve Question 4

Simplify \(\frac{10}{10}=1\), so the decimal is 1.0.

Step5: Solve Question 5

Convert \(\frac{3}{5}\) to a decimal by dividing 3 by 5: \(3\div5 = 0.6\).

Step6: Solve Question 6

Convert \(1\frac{3}{10}\) to an improper fraction: \(1\frac{3}{10}=\frac{13}{10}\). Divide 13 by 10: \(13\div10 = 1.3\).

Step7: Solve Question 7

Convert \(\frac{7}{10}\) to a decimal by dividing 7 by 10: \(7\div10 = 0.7\).

Step8: Solve Question 8

Simplify \(\frac{0}{10}=0\), so the decimal is 0.0.

Step9: Solve Question 9

\(\frac{2}{2}=1\), looking at the number line (A at 0, B, C, D, E, F, G, H, 1 at the end), the point for 1 should be the last one, but maybe a typo? Wait, \(\frac{2}{2}=1\), on the second number line (from 0 to 2), 1 is at the middle? Wait, the second number line has A at 0, then B, C, D, E (at 1), F, G, H, 1 at the end (which is 2? Wait, no, the number line is from 0 to 2, with 1 at the middle (E). Wait, \(\frac{2}{2}=1\), so it's at E? Wait, maybe I misread. Wait, the second number line: A(0), B, C, D, E(1), F, G, H, 1 (which is 2? No, the label is 1 and 2 at the end. Wait, maybe the number line is from 0 to 2, with 1 at E. So \(\frac{2}{2}=1\), so the letter is E.

Step10: Solve Question 10

Simplify \(1\frac{4}{8}=1\frac{1}{2}=1.5\). On the number line from 0 to 2, 1.5 is halfway between 1 and 2, so maybe H? Wait, the number line has A(0), B, C, D, E(1), F, G, H, 1 (2). Wait, 1.5 is between E(1) and the end (2), so H? Wait, maybe the spacing: from 0 to 2, divided into 8 parts? Wait, \(1\frac{4}{8}=1.5\), so on the number line, if E is at 1, then F, G, H: H is at 1.5? So 10. \(1\frac{4}{8}\) is H?

Step11: Solve Question 11

Simplify \(1\frac{2}{8}=1\frac{1}{4}=1.25\). On the number line, between E(1) and F, G, H. 1.25 is between 1 and 1.5, so maybe G? Wait, maybe the number line is divided into eighths? Wait, \(1\frac{2}{8}=1.25\), so from 1 (E), each mark is 0.25? So E(1), F(1.25), G(1.5), H(1.75)? Wait, no, maybe my initial assumption is wrong. Wait, the second number line: A(0), B, C, D, E(1), F, G, H, 1 (2). If we consider each segment as 0.25 (since from 0 to 2 is 8 segments? No, 0 to 2 is 2 units, with 8 marks? Wait, A(0), B(0.25), C(0.5), D(0.75), E(1), F(1.25), G(1.5), H(1.75), 1(2). Ah, that makes sense. So \(1\frac{2}{8}=1.25\), which is F.

Step12: Solve Question 12

Simplify \(\frac{6}{3}=2\), so on the number line from 0 to 2, the end is 2, so the letter is the last one (the one labeled 1, but it's 2). So the letter is the last point (the one at 2).

Step13: Solve Question 13

1.75 is on the number line. From the number line with A(0), B, C, D, E(1), F, G, H, 1(2). If each segment is 0.25, then H is at 1.75 (since E(1), F(1.25), G(1.5), H(1.75)). So 13. 1.75 is H.

Step14: Solve Question 14

\(\frac{1}{4}=0.25\), on the number line, B is at 0.25? So 14. \(\frac{1}{4}\) is B.

Step15: Solve Question 15

0.75 is on the number line. D is at 0.75 (A(0), B(0.25), C(0.5), D(0.75), E(1)). So 15. 0.75 is D.

Step16: Solve Question 16

Simplify \(\frac{6}{12}=0.5\), on the number line, C is at 0.5 (A(0), B(0.25), C(0.5), D(0.75), E(1)). So 16. \(\frac{6}{12}\) is C.

Step17: Solve Question 17

0.2. Convert each fraction: \(\frac{1}{5}=0.2\), \(\frac{1}{2}=0.5\), \(\frac{2}{10}=0.2\). Wait, the options are \(\frac{1}{5}\), \(\frac{1}{2}\), \(\frac{2}{10}\). 0.2 is equal to \(\frac{1}{5}\) and \(\frac{2}{10}\), but circle the fraction. So \(\frac{1}{5}\) or \(\frac{2}{10}\). But the problem says "circle the fraction or mixed number", so \(\frac{1}{5}\) (since \(\frac{2}{10}\) can be simplified, but both are equivalent. Wait, 0.2 = \(\frac{1}{5}\), so circle \(\frac{1}{5}\).

Step18: Solve Question 18

0.4. Convert fractions: \(\frac{1}{4}=0.25\), \(\frac{2}{5}=0.4\), \(\frac{6}{10}=0.6\). So circle \(\frac{2}{5}\).

Step19: Solve Question 19

1.4. Convert mixed numbers: \(1\frac{1}{4}=1.25\), \(1\frac{2}{5}=1.4\), \(1\frac{14}{10}=2.4\). So circle \(1\frac{2}{5}\).

Step20: Solve Question 20

0.9. Convert fractions: \(\frac{1}{9}\approx0.11\), \(\frac{9}{1}=9\), \(\frac{9}{10}=0.9\). So circle \(\frac{9}{10}\).

Step21: Solve Question 21

0.8. Convert fractions: \(\frac{1}{8}=0.125\), \(\frac{8}{10}=0.8\), \(\frac{10}{8}=1.25\). So circle \(\frac{8}{10}\).

Step22: Solve Question 22

2.1. Convert: \(\frac{2}{1}=2\), \(2\frac{1}{10}=2.1\), \(2\frac{21}{10}=4.1\). So circle \(2\frac{1}{10}\).

Step23: Solve Question 23

1.2. Convert mixed numbers: \(1\frac{1}{2}=1.5\), \(1\frac{1}{5}=1.2\), \(1\frac{2}{12}\approx1.166\). So circle \(1\frac{1}{5}\).

Step24: Solve Question 24

0. Convert: \(\frac{0}{1}=0\), \(\frac{1}{1}=1\), \(\frac{1}{10}=0.1\). So circle \(\frac{0}{1}\).

Step25: Solve Question 25

4.5. Convert: \(4\frac{5}{1}=4.5\)? No, \(4\frac{5}{1}=9\). Wait, \(4\frac{5}{10}=4.5\), \(\frac{45}{10}=4.5\). So circle \(4\frac{5}{10}\) (or \(\frac{45}{10}\), but \(4\frac{5}{10}\) is a mixed number).

Step26: Solve Question 26

\(2\frac{3}{4}=2.75\). The number line is from 0 to 4, with 0, 1, 2, 3, 4. The marks: A(0), B, C, D, E(1), F, G, H, I(2), J, K, L, M(3), N, O, P, Q(4). Each segment is 0.25? From 2 (I) to 3 (M) is 1 unit, divided into 4 parts (J, K, L, M). So 2.75 is 3 - 0.25, so M is at 3, N is at 3.25? Wait, no, \(2\frac{3}{4}=2.75\), which is between 2 and 3, 0.75 from 2. So from I(2), each mark is 0.25: I(2), J(2.25), K(2.5), L(2.75), M(3). So the letter is L. Explanation: \(2\frac{3}{4}=2.75\). The number line from 0 to 4 has I at 2. Each subsequent mark (J, K, L, M) is 0.25 apart. So 2 + 0.75 = 2.75, which is at L.

Answer:

1. \(0.5\)
2. \(1.2\)
3. \(1.4\)
4. \(1.0\)
5. \(0.6\)
6. \(1.3\)
7. \(0.7\)
8. \(0.0\)
9. \(E\)
10. \(H\) (or as per correct number line interpretation)
11. \(F\) (or as per correct number line interpretation)
12. The last point (labeled 1, representing 2)
13. \(H\)
14. \(B\)
15. \(D\)
16. \(C\)
17. \(\frac{1}{5}\) (circled)
18. \(\frac{2}{5}\) (circled)
19. \(1\frac{2}{5}\) (circled)
20. \(\frac{9}{10}\) (circled)
21. \(\frac{8}{10}\) (circled)
22. \(2\frac{1}{10}\) (circled)
23. \(1\frac{1}{5}\) (circled)
24. \(\frac{0}{1}\) (circled)
25. \(4\frac{5}{10}\) (circled)
26. \(L\) (Explanation: \(2\frac{3}{4}=2.75\), located 0.75 above 2 on the number line, corresponding to letter \(L\) as each segment after 2 is 0.25, so 2 + 0.75 = 2.75 at \(L\))

(Note: For questions 9 - 16, the exact letter may depend on the precise spacing of the number line, but the above is a reasoned approach. For the circling questions, the circled fraction/mixed number is the equivalent one.)