Equivalent Fractions & Addition, Subtraction, Multiplication, and ... - Free Printable
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Step-by-step solution for: Equivalent Fractions & Addition, Subtraction, Multiplication, and ...
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Show Answer Key & Explanations
Step-by-step solution for: Equivalent Fractions & Addition, Subtraction, Multiplication, and ...
It looks like you've uploaded a worksheet titled "Cumulative Review" with several math problems involving fractions, decimals, and operations (addition, subtraction, multiplication, and division). However, since I can't view images directly, I’ll need you to describe the content or type out the problems if they are not already visible in text form.
But based on your message, it seems the image contains a list of math problems. Let me go ahead and solve them as they appear in your description, assuming the following:
---
25. $ \frac{6}{7} = \frac{24}{?} $
We want to find the denominator that makes this fraction equivalent to $ \frac{6}{7} $.
Since $ 6 \times 4 = 24 $, we must multiply the denominator by 4:
$ 7 \times 4 = 28 $
✔ Answer: 28
---
26. $ \frac{3}{8} = \frac{?}{24} $
We want to find the numerator such that the fraction equals $ \frac{3}{8} $.
Since $ 8 \times 3 = 24 $, we multiply numerator by 3:
$ 3 \times 3 = 9 $
✔ Answer: 9
---
27. $ \frac{8}{15} = \frac{?}{45} $
$ 15 \times 3 = 45 $, so multiply numerator by 3:
$ 8 \times 3 = 24 $
✔ Answer: 24
---
28. $ \frac{6}{7} = \frac{?}{42} $
$ 7 \times 6 = 42 $, so multiply numerator by 6:
$ 6 \times 6 = 36 $
✔ Answer: 36
---
39. $ 6.002 + 12.5 $
Align decimals:
```
6.002
+12.500
-------
18.502
```
✔ Answer: 18.502
---
40. $ 31.426 + 25.8 $
Align decimals:
```
31.426
+25.800
--------
57.226
```
✔ Answer: 57.226
---
43. $ 4.35 - 2.005 $
Align decimals:
```
4.350
- 2.005
-------
2.345
```
✔ Answer: 2.345
---
44. $ 28.54 - 1.052 $
Align decimals:
```
28.540
- 1.052
-------
27.488
```
✔ Answer: 27.488
---
46. $ 9.891 - 1.2 $ → Wait! This is subtraction, but labeled "Multiply". Likely a typo.
Wait — problem says “Multiply the decimals”, but #46 is written as 9.891 - 1.2, which is subtraction.
Let’s check again:
Actually, the list shows:
46. 9.891 - 1.2 → this should be subtraction, but section title says "Multiply".
Possibly a mislabeling. Let's assume:
46. 9.891 × 1.2
Let’s compute:
First, ignore decimals:
$ 9891 × 12 = ? $
Break it down:
$ 9891 × 10 = 98,910 $
$ 9891 × 2 = 19,782 $
Total: $ 98,910 + 19,782 = 118,692 $
Now count decimal places:
9.891 has 3, 1.2 has 1 → total 4 decimal places
So: $ 11.8692 $
✔ Answer: 11.8692
---
47. $ 6.2 × 12.43 $
Compute:
$ 6.2 × 12.43 $
First: $ 62 × 1243 = ? $
Or easier:
$ 6.2 × 12.43 = (6 + 0.2) × 12.43 = 6×12.43 + 0.2×12.43 $
$ 6 × 12.43 = 74.58 $
$ 0.2 × 12.43 = 2.486 $
Sum: $ 74.58 + 2.486 = 77.066 $
✔ Answer: 77.066
---
48. $ 25 × 1.75 $
$ 25 × 1.75 = 25 × (1 + 0.75) = 25 + 18.75 = 43.75 $
Alternatively:
$ 25 × 1.75 = 25 × \frac{7}{4} = \frac{175}{4} = 43.75 $
✔ Answer: 43.75
---
49. $ 2.5 × .175 $
Note: $ .175 = 0.175 $
$ 2.5 × 0.175 $
Convert:
$ 2.5 × 0.175 = \frac{5}{2} × \frac{7}{40} = \frac{35}{80} = \frac{7}{16} = 0.4375 $
Or compute:
$ 2.5 × 0.175 = 0.4375 $
✔ Answer: 0.4375
---
50. $ 1.008 × 16.2 $
Use multiplication:
$ 1.008 × 16.2 $
Break it down:
$ 1.008 × 16 = 16.128 $
$ 1.008 × 0.2 = 0.2016 $
Add: $ 16.128 + 0.2016 = 16.3296 $
✔ Answer: 16.3296
---
51. $ 3.12 ÷ 4.4 $
To divide decimals, eliminate decimals by multiplying numerator and denominator by 10:
$ \frac{3.12}{4.4} = \frac{31.2}{44} $
Now divide:
$ 31.2 ÷ 44 $
$ 44 × 0.7 = 30.8 $, remainder $ 0.4 $
$ 0.4 ÷ 44 = 0.00909... $ → approx $ 0.70909 $
Better: do long division:
$ 31.2 ÷ 44 $
→ $ 0.70909... $
So $ 3.12 ÷ 4.4 ≈ 0.7091 $ (rounded to 4 decimal places)
✔ Answer: ~0.7091
---
52. $ 1.25 ÷ 2.5 $
$ \frac{1.25}{2.5} = \frac{125}{250} = \frac{1}{2} = 0.5 $
✔ Answer: 0.5
---
53. $ 0.48 ÷ 8 $
$ 0.48 ÷ 8 = 0.06 $
✔ Answer: 0.06
---
54. $ 16.4 ÷ 82 $
$ 16.4 ÷ 82 $
Try: $ 82 × 0.2 = 16.4 $
✔ Answer: 0.2
---
| Problem | Answer |
|--------|--------|
| 25 | 28 |
| 26 | 9 |
| 27 | 24 |
| 28 | 36 |
| 39 | 18.502 |
| 40 | 57.226 |
| 43 | 2.345 |
| 44 | 27.488 |
| 46 | 11.8692 |
| 47 | 77.066 |
| 48 | 43.75 |
| 49 | 0.4375 |
| 50 | 16.3296 |
| 51 | ~0.7091 |
| 52 | 0.5 |
| 53 | 0.06 |
| 54 | 0.2 |
> ⚠️ Note: Problem #46 was written as subtraction, but likely meant to be multiplication. If it was truly subtraction, then:
> $ 9.891 - 1.2 = 8.691 $
>
> But given the section header "Multiply", it's more likely a typo and intended as multiplication.
Let me know if you'd like these checked further or formatted differently!
But based on your message, it seems the image contains a list of math problems. Let me go ahead and solve them as they appear in your description, assuming the following:
---
Fill in the missing part of each pair of fractions to make them equivalent:
25. $ \frac{6}{7} = \frac{24}{?} $
We want to find the denominator that makes this fraction equivalent to $ \frac{6}{7} $.
Since $ 6 \times 4 = 24 $, we must multiply the denominator by 4:
$ 7 \times 4 = 28 $
✔ Answer: 28
---
26. $ \frac{3}{8} = \frac{?}{24} $
We want to find the numerator such that the fraction equals $ \frac{3}{8} $.
Since $ 8 \times 3 = 24 $, we multiply numerator by 3:
$ 3 \times 3 = 9 $
✔ Answer: 9
---
27. $ \frac{8}{15} = \frac{?}{45} $
$ 15 \times 3 = 45 $, so multiply numerator by 3:
$ 8 \times 3 = 24 $
✔ Answer: 24
---
28. $ \frac{6}{7} = \frac{?}{42} $
$ 7 \times 6 = 42 $, so multiply numerator by 6:
$ 6 \times 6 = 36 $
✔ Answer: 36
---
Add the decimals:
39. $ 6.002 + 12.5 $
Align decimals:
```
6.002
+12.500
-------
18.502
```
✔ Answer: 18.502
---
40. $ 31.426 + 25.8 $
Align decimals:
```
31.426
+25.800
--------
57.226
```
✔ Answer: 57.226
---
Subtract the decimals:
43. $ 4.35 - 2.005 $
Align decimals:
```
4.350
- 2.005
-------
2.345
```
✔ Answer: 2.345
---
44. $ 28.54 - 1.052 $
Align decimals:
```
28.540
- 1.052
-------
27.488
```
✔ Answer: 27.488
---
Multiply the decimals:
46. $ 9.891 - 1.2 $ → Wait! This is subtraction, but labeled "Multiply". Likely a typo.
Wait — problem says “Multiply the decimals”, but #46 is written as 9.891 - 1.2, which is subtraction.
Let’s check again:
Actually, the list shows:
46. 9.891 - 1.2 → this should be subtraction, but section title says "Multiply".
Possibly a mislabeling. Let's assume:
46. 9.891 × 1.2
Let’s compute:
First, ignore decimals:
$ 9891 × 12 = ? $
Break it down:
$ 9891 × 10 = 98,910 $
$ 9891 × 2 = 19,782 $
Total: $ 98,910 + 19,782 = 118,692 $
Now count decimal places:
9.891 has 3, 1.2 has 1 → total 4 decimal places
So: $ 11.8692 $
✔ Answer: 11.8692
---
47. $ 6.2 × 12.43 $
Compute:
$ 6.2 × 12.43 $
First: $ 62 × 1243 = ? $
Or easier:
$ 6.2 × 12.43 = (6 + 0.2) × 12.43 = 6×12.43 + 0.2×12.43 $
$ 6 × 12.43 = 74.58 $
$ 0.2 × 12.43 = 2.486 $
Sum: $ 74.58 + 2.486 = 77.066 $
✔ Answer: 77.066
---
48. $ 25 × 1.75 $
$ 25 × 1.75 = 25 × (1 + 0.75) = 25 + 18.75 = 43.75 $
Alternatively:
$ 25 × 1.75 = 25 × \frac{7}{4} = \frac{175}{4} = 43.75 $
✔ Answer: 43.75
---
49. $ 2.5 × .175 $
Note: $ .175 = 0.175 $
$ 2.5 × 0.175 $
Convert:
$ 2.5 × 0.175 = \frac{5}{2} × \frac{7}{40} = \frac{35}{80} = \frac{7}{16} = 0.4375 $
Or compute:
$ 2.5 × 0.175 = 0.4375 $
✔ Answer: 0.4375
---
50. $ 1.008 × 16.2 $
Use multiplication:
$ 1.008 × 16.2 $
Break it down:
$ 1.008 × 16 = 16.128 $
$ 1.008 × 0.2 = 0.2016 $
Add: $ 16.128 + 0.2016 = 16.3296 $
✔ Answer: 16.3296
---
Divide the decimals:
51. $ 3.12 ÷ 4.4 $
To divide decimals, eliminate decimals by multiplying numerator and denominator by 10:
$ \frac{3.12}{4.4} = \frac{31.2}{44} $
Now divide:
$ 31.2 ÷ 44 $
$ 44 × 0.7 = 30.8 $, remainder $ 0.4 $
$ 0.4 ÷ 44 = 0.00909... $ → approx $ 0.70909 $
Better: do long division:
$ 31.2 ÷ 44 $
→ $ 0.70909... $
So $ 3.12 ÷ 4.4 ≈ 0.7091 $ (rounded to 4 decimal places)
✔ Answer: ~0.7091
---
52. $ 1.25 ÷ 2.5 $
$ \frac{1.25}{2.5} = \frac{125}{250} = \frac{1}{2} = 0.5 $
✔ Answer: 0.5
---
53. $ 0.48 ÷ 8 $
$ 0.48 ÷ 8 = 0.06 $
✔ Answer: 0.06
---
54. $ 16.4 ÷ 82 $
$ 16.4 ÷ 82 $
Try: $ 82 × 0.2 = 16.4 $
✔ Answer: 0.2
---
✔ Final Answers Summary:
| Problem | Answer |
|--------|--------|
| 25 | 28 |
| 26 | 9 |
| 27 | 24 |
| 28 | 36 |
| 39 | 18.502 |
| 40 | 57.226 |
| 43 | 2.345 |
| 44 | 27.488 |
| 46 | 11.8692 |
| 47 | 77.066 |
| 48 | 43.75 |
| 49 | 0.4375 |
| 50 | 16.3296 |
| 51 | ~0.7091 |
| 52 | 0.5 |
| 53 | 0.06 |
| 54 | 0.2 |
> ⚠️ Note: Problem #46 was written as subtraction, but likely meant to be multiplication. If it was truly subtraction, then:
> $ 9.891 - 1.2 = 8.691 $
>
> But given the section header "Multiply", it's more likely a typo and intended as multiplication.
Let me know if you'd like these checked further or formatted differently!
Parent Tip: Review the logic above to help your child master the concept of add subtract multiply and divide decimals worksheet.