Math online exercise for grade 7 - Free Printable

Let's solve each question step by step and explain the reasoning.

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Q1: Compare. Use the symbols: <, >, and =.

We compare integers using a number line:
- Numbers to the right are greater.
- Negative numbers are less than positive numbers.
- Among negative numbers, the one with the smaller absolute value is greater (closer to zero).

a. 3 ___ -5
3 is positive, -5 is negative → 3 > -5
✔ Answer: 3 > -5

b. -10 ___ 0
Negative numbers are less than zero → -10 < 0
✔ Answer: -10 < 0

c. -7 ___ 7
-7 is negative, 7 is positive → -7 < 7
✔ Answer: -7 < 7

d. -1 ___ -1
Same number → equal
✔ Answer: -1 = -1

e. -8 ___ -2
Both negative; compare absolute values: |−8| = 8, |−2| = 2
Since 8 > 2, −8 < −2
✔ Answer: -8 < -2

f. 14 ___ -15
Positive vs negative → 14 > -15
✔ Answer: 14 > -15

g. -56 ___ -58
Both negative; |−56| = 56, |−58| = 58
Since 56 < 58 → −56 > −58
✔ Answer: -56 > -58

h. 43 ___ 34
43 > 34 (both positive)
✔ Answer: 43 > 34

i. -16 ___ 15
Negative vs positive → -16 < 15
✔ Answer: -16 < 15

j. -354 ___ -345
Both negative; |−354| = 354, |−345| = 345
354 > 345 → so −354 < −345
✔ Answer: -354 < -345

k. 789 ___ -798
Positive vs negative → 789 > -798
✔ Answer: 789 > -798

l. -605 ___ -655
Both negative; |−605| = 605, |−655| = 655
605 < 655 → so −605 > −655
✔ Answer: -605 > -655

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Q2: Circle the integer with the greatest value.

We identify the largest number in each pair.

a. 4, -5
4 > -5 → ✔ 4

b. -16, -14
Both negative; |−16| = 16, |−14| = 14 → −14 is closer to zero → −14 > −16
✔ -14

c. -22, 0
0 > -22 → ✔ 0

d. -51, 7
7 is positive → 7 > -51 → ✔ 7

e. 57, 75
75 > 57 → ✔ 75

f. -290, -209
Both negative; |−290| = 290, |−209| = 209 → −209 > −290
✔ -209

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Q3: Answer the questions.

s. Which is colder: −3°F or 0°F?
Lower temperature = colder
−3°F < 0°F → so −3°F is colder
✔ Answer: −3°F

t. Which is warmer: −13°C or −10°C?
Higher temperature = warmer
−10°C > −13°C → so −10°C is warmer
✔ Answer: −10°C

u. Which is a higher elevation? 40 feet below sea level or 14 feet below sea level?
Below sea level = negative
40 ft below = −40 ft
14 ft below = −14 ft
−14 > −40 → so −14 is higher (closer to zero)
✔ Answer: 14 feet below sea level

v. Which is a higher elevation? 2 feet below sea level or 1 foot above sea level?
2 ft below = −2 ft
1 ft above = +1 ft
+1 > −2 → so 1 foot above is higher
✔ Answer: 1 foot above sea level

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✔ Final Answers:

#### Q1:
a. 3 > -5
b. -10 < 0
c. -7 < 7
d. -1 = -1
e. -8 < -2
f. 14 > -15
g. -56 > -58
h. 43 > 34
i. -16 < 15
j. -354 < -345
k. 789 > -798
l. -605 > -655

#### Q2:
a. 4
b. -14
c. 0
d. 7
e. 75
f. -209

#### Q3:
s. −3°F
t. −10°C
u. 14 feet below sea level
v. 1 foot above sea level

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