5-A-Day Math Review: Week 1 worksheet with math problems for Monday and Tuesday.

Let’s go step by step through each problem on the worksheet.

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Monday, Problem 1: Express the ratio in three different ways (grey to white)

We see 2 grey circles and 3 white circles.

So the ratio of grey to white is 2 to 3.

Three ways to write it:

- As a fraction: 2/3
- Using “to”: 2 to 3
- Using a colon: 2 : 3

✔ All correct.

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Monday, Problem 2: Integer, Opposite, Absolute Value

Remember:
- The opposite of a number is its negative (if positive) or positive (if negative). So opposite of 3 is -3, opposite of -4 is 4, etc.
- The absolute value is how far the number is from zero — always positive. So |3| = 3, |-4| = 4, |8| = 8.

Fill in the table:

| Integer | Opposite | Absolute Value |
|---------|----------|----------------|
| 3 | -3 | 3 |
| -4 | 4 | 4 |
| 8 | -8 | 8 |

✔ Done.

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Monday, Problem 3: Write an expression for “A number n divided by 6”

That means: take the number n, and divide it by 6.

Expression: n ÷ 6 or n/6

Either is fine. We’ll use n/6 since it’s common in math.

✔ Answer: n/6

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Monday, Problem 4: Solve. Show your work.

First: 27.9 + 212.5

Add them:

27.9
+212.5
= 240.4

Second: 175.5 - 12.7

Subtract:

175.5
- 12.7
= 162.8

✔ Answers: 240.4 and 162.8

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Monday, Problem 5: Division and Multiplication

First: 975 ÷ 6

Do long division:

6 into 9 → 1, remainder 3
Bring down 7 → 37
6 into 37 → 6 (6×6=36), remainder 1
Bring down 5 → 15
6 into 15 → 2 (6×2=12), remainder 3
Add decimal point, bring down 0 → 30
6 into 30 → 5

So: 162.5

Check: 6 × 162.5 = 975 ✔

Second: 478 × 38

Break it down:

478 × 30 = 14,340
478 × 8 = 3,824
Add: 14,340 + 3,824 = 18,164

✔ Answer: 18,164

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Tuesday, Problem 1: 4 shirts for $32.00

Rate = total cost / number of items = $32.00 / 4 shirts = $8 per shirt

Unit rate is the same as rate here — cost per one item.

So:

rate = $32.00 for 4 shirts
unit rate = $8.00 per shirt

✔ Done.

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Tuesday, Problem 2: Grid with shaded squares

The grid has 10 rows and 10 columns → 100 small squares total.

Shaded part: Let’s count.

It looks like 3 full columns are shaded → 3 × 10 = 30 squares.

So:

Fraction: 30/100 → simplify? Not needed unless asked. But we can reduce to 3/10 if wanted. Since question doesn’t say, leave as 30/100 or simplify? Usually they want simplified. Let’s do both.

Actually, looking at standard practice, they often expect simplified fraction.

30/100 = 3/10

Decimal: 30 ÷ 100 = 0.30 or just 0.3

Ratio: shaded to total → 30:100 or simplified 3:10

Percent: 30 out of 100 = 30%

✔ Answers:

Fraction: 3/10
Decimal: 0.3
Ratio: 3:10
Percent: 30%

*(Note: If they didn’t simplify, 30/100, 0.30, 30:100, 30% would also be acceptable, but simplified is better.)*

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Tuesday, Problem 3: What is 50% of 80?

Use the proportion:

part / whole = percent / 100

So:

part / 80 = 50 / 100

Cross multiply:

part × 100 = 80 × 50
part × 100 = 4000
part = 4000 ÷ 100 = 40

Or easier: 50% is half → half of 80 is 40.

✔ Answer: 40

In the boxes:

part → 40
whole → 80
percent → 50

So: 40/80 = 50/100

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Tuesday, Problem 4: Ken grew 4/5 inch, Sang grew 3/8 inch. Who grew more and by how much?

Compare 4/5 and 3/8.

Find common denominator. LCM of 5 and 8 is 40.

Convert:

4/5 = (4×8)/(5×8) = 32/40
3/8 = (3×5)/(8×5) = 15/40

32/40 > 15/40 → Ken grew more.

Difference: 32/40 - 15/40 = 17/40 inch

✔ Answer: Ken grew more by 17/40 inch

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Tuesday, Problem 5: Complete the table and graph y = x + 2

Equation: y = x + 2

Given:

When x = 0, y = 0 + 2 = 2 → already filled

When x = 1, y = 1 + 2 = 3

When x = 2, y = 2 + 2 = 4

You can add more points if you want, but table only shows up to x=2.

Table:

| x | y |
|---|---|
| 0 | 2 |
| 1 | 3 |
| 2 | 4 |

Now graph: Plot (0,2), (1,3), (2,4) and draw a straight line through them.

✔ Table complete.

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Final Answers Summary:

Monday:

1. Ratio: 2/3, 2 to 3, 2:3
2. Table:
- 3 → opposite -3, abs 3
- -4 → opposite 4, abs 4
- 8 → opposite -8, abs 8
3. Expression: n/6
4. 27.9 + 212.5 = 240.4; 175.5 - 12.7 = 162.8
5. 975 ÷ 6 = 162.5; 478 × 38 = 18,164

Tuesday:

1. rate = $32.00 for 4 shirts; unit rate = $8.00 per shirt
2. Fraction: 3/10; Decimal: 0.3; Ratio: 3:10; Percent: 30%
3. 50% of 80 = 40 → part=40, whole=80, percent=50
4. Ken grew more by 17/40 inch
5. Table: x=1→y=3; x=2→y=4; graph points (0,2), (1,3), (2,4)

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Final Answer:
All problems solved correctly as shown above.