Class 7 Maths Worksheet: Rational Numbers Addition - Practice Problems for Students

Let’s solve each problem step by step. We’re adding rational numbers — that means fractions, including negative ones. When denominators are the same, we just add numerators. When they’re different, we find a common denominator first.

Also note: The worksheet says to put answers in brackets, like (-8/5). So we’ll do that.

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1. (-5/7) + (3/7)
Same denominator → add numerators: -5 + 3 = -2
Answer: (-2/7)

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2. (-15/4) + (7/4)
Same denominator → -15 + 7 = -8
So: -8/4 = -2
But write as fraction? Worksheet example uses fraction form even if whole number? Example was (-8/5), so maybe keep as fraction unless it simplifies to integer? But -8/4 is exactly -2. Let’s check instruction: “Provide the answers in brackets. Eg. (-8/5)” — doesn’t say must be improper or reduced. But usually we simplify. Since -8/4 = -2, and -2 is an integer, but rational numbers include integers. However, to match format, perhaps write as (-2/1)? But that’s not typical. Looking at problem 6: -3 + (3/5) — that will be mixed. Probably better to leave as simplified fraction or integer if exact.

Wait — let’s see problem 6: -3 + 3/5. That’s not same denominator. So for consistency, maybe always write as single fraction? But -8/4 reduces to -2. I think writing (-2) is acceptable, but to follow example strictly, maybe write as (-8/4)? No, that’s not simplified. Better to simplify.

Actually, looking at other problems, like #3: (-8/11)+(-4/11)= -12/11 → which is already simplified. So for #2: -8/4 = -2 → so answer should be (-2). But let’s confirm with standard practice. In math worksheets, if it simplifies to integer, you write the integer. And since rational numbers include integers, it’s fine. Also, the example (-8/5) is just an example of format, not implying all answers must be non-integer.

I’ll go with simplified form.

So: (-2)

But wait — let me double-check the instruction: “Provide the answers in brackets. Eg. (-8/5)” — the example has a slash, but that’s because it’s a fraction. If answer is integer, probably just (-2). To be safe, I’ll check similar problems online or standard practice — but since I can’t, I’ll assume simplified form is expected.

Alternatively, maybe they want all as fractions? Problem 6: -3 + 3/5 = -15/5 + 3/5 = -12/5 → which is fraction. So for #2, -8/4 could be left as (-8/4) but that’s not reduced. Usually we reduce.

I think best is to reduce fully. So:

#2: (-15/4)+(7/4)= (-8/4) = -2 → so (-2)

But let’s proceed and see.

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3. (-8/11) + (-4/11)
Same denominator: -8 + (-4) = -12
Answer: (-12/11)

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4. (6/13) + (-9/13)
6 + (-9) = -3
Answer: (-3/13)

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5. (3/4) + (-3/5)
Different denominators. LCM of 4 and 5 is 20.

Convert:
3/4 = (3×5)/(4×5) = 15/20
-3/5 = (-3×4)/(5×4) = -12/20

Add: 15/20 + (-12/20) = 3/20
Answer: (3/20)

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6. -3 + (3/5)
Write -3 as fraction with denominator 5: -3 = -15/5
Then: -15/5 + 3/5 = (-15 + 3)/5 = -12/5
Answer: (-12/5)

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7. (-7/27) + (11/18)
Find LCM of 27 and 18.

Factors:
27 = 3³
18 = 2 × 3²
LCM = 2 × 3³ = 54

Convert:
-7/27 = (-7 × 2)/(27 × 2) = -14/54
11/18 = (11 × 3)/(18 × 3) = 33/54

Add: -14/54 + 33/54 = 19/54
Answer: (19/54)

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8. (31/-4) + (-5/8)
First, 31/-4 is same as -31/4.

So: -31/4 + (-5/8)

LCM of 4 and 8 is 8.

-31/4 = (-31 × 2)/(4 × 2) = -62/8
-5/8 remains -5/8

Add: -62/8 + (-5/8) = -67/8
Answer: (-67/8)

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9. (-9/4) + (6/7)
LCM of 4 and 7 is 28.

-9/4 = (-9 × 7)/(4 × 7) = -63/28
6/7 = (6 × 4)/(7 × 4) = 24/28

Add: -63/28 + 24/28 = -39/28
Answer: (-39/28)

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10. (-9/14) + (2/7)
LCM of 14 and 7 is 14.

-9/14 remains
2/7 = (2 × 2)/(7 × 2) = 4/14

Add: -9/14 + 4/14 = -5/14
Answer: (-5/14)

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Now, back to #2: (-15/4) + (7/4) = -8/4 = -2. Should we write as (-2) or (-8/4)? Since the example given is (-8/5), which is unreduced? No, -8/5 is already reduced. But -8/4 reduces to -2. In most math contexts, we simplify fractions. Also, in problem 6, we got -12/5 which is already simplified. For consistency, I think we should simplify where possible.

Moreover, if we look at problem 3: -12/11 is fine as is. Problem 4: -3/13. All others are simplified.

For #2, -8/4 simplifies to -2, so answer should be (-2).

But let me check: is there any chance they want improper fractions only? The example (-8/5) is improper, but that’s because it couldn’t be simplified. Here it can.

I think (-2) is correct.

To match bracket format, write as (-2).

Similarly, if any answer is positive integer, like if we had 8/4=2, we’d write (2). But here it’s negative.

So final decision: #2 is (-2)

Now, compiling all answers:

1. (-2/7)
2. (-2)
3. (-12/11)
4. (-3/13)
5. (3/20)
6. (-12/5)
7. (19/54)
8. (-67/8)
9. (-39/28)
10. (-5/14)

Wait — for #2, is (-2) acceptable? Or should it be (-2/1)? I think (-2) is fine, as it's a rational number.

But let me see the worksheet again mentally: the example is (-8/5), which is a fraction. But in mathematics, integers are rational numbers, and we often write them without denominator.

Moreover, in problem 6, we have -3 which is integer, and we converted to fraction, but the answer came out as fraction. For #2, it simplifies to integer.

I recall that in some curricula, they prefer to write all answers as fractions, even if integer. But that would be unusual.

Another way: look at problem 8: (31/-4) which is -31/4, and we wrote (-67/8), which is fine.

Perhaps for #2, since -8/4 = -2, and -2 is simpler, we use that.

I think it's safe.

But to be absolutely sure, let's calculate numerically:

-15/4 = -3.75, 7/4=1.75, sum = -2.0 → so -2.

Yes.

Final Answers:

1. (-2/7)
2. (-2)
3. (-12/11)
4. (-3/13)
5. (3/20)
6. (-12/5)
7. (19/54)
8. (-67/8)
9. (-39/28)
10. (-5/14)

In the response, I need to list them clearly.

The user didn't ask for explanation, so according to rules, since ExplainAnswer=false, TeachTopic=false, GeneratePractice=false, I should only provide Final Answer section.

But the instruction says: "Complete ALL reasoning and explanations BEFORE writing the Final Answer." and then "If an option is false, completely omit that section."

So since all options are false, I omit Explanation, TeachTopic, PracticeTask sections, and only give Final Answer.

But the Final Answer should contain the answers to all 10 problems.

How to format? Probably list them numbered.

Also, ensure brackets as per instruction.

So:

Final Answer:
1. (-2/7)
2. (-2)
3. (-12/11)
4. (-3/13)
5. (3/20)
6. (-12/5)
7. (19/54)
8. (-67/8)
9. (-39/28)
10. (-5/14)

For #2, I'm still slightly unsure. Let me think if there's a convention.

Upon second thought, in many school worksheets, when the result is an integer, they write the integer. For example, if you add -4/2 + 2/2 = -2/2 = -1, they write -1.

Moreover, the example (-8/5) is just to show the bracket format, not that all answers must have denominator.

So I'll stick with (-2) for #2.

Another point: in problem 6, -3 + 3/5, we got -12/5, which is correct, and not written as mixed number, so consistent.

All good.

So final answer list.