UK Secondary (7-11)
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Equivalent number sentences
Lesson

Number sentences are a way of describing a situation using mathematics.  Like written sentences, number sentences have some specific structure.  Specifically they must have an equal sign and the value on either side of the equal sign must be the same.  

In maths, we also call number sentences equations, 

We can think of number sentences like scales. The equals sign is the middle of the scales

However, different combinations of numbers can add up to the same amount. For example, $6+4$6+4 adds up to $10$10 but $5+5$5+5 also equals $10$10.

The law of transitivity states that if $a=b$a=b and $a=c$a=c, then $b=c$b=c.

Using our example, we can say that if $6+4=10$6+4=10 and $5+5=10$5+5=10, then $6+4=5+5$6+4=5+5

 

Examples

Question 1

Which of the following is a correct number sentence?

A) $8+19=34+7$8+19=34+7     B) $8+19=20+7$8+19=20+7     C)  $8+19=23+7$8+19=23+7     D)  $8+19=-20+7$8+19=20+7

Think: In which of these equations is the left hand side equal to the right hand side?

Do:

 $8+19$8+19 $=$= $27$27 Which other option also equals $27$27?
       
$34+7$34+7 $=$= $31$31  
$20+7$20+7 $=$= $27$27 This one!
$23+7$23+7 $=$= $30$30  
$-20+7$20+7 $=$= $-13$13  

So B) $8+19=20+7$8+19=20+7 is the correct option.

 

Question 2

Which of the following is a correct number sentence?

A) $\left(8+10\right)\times10=49-131$(8+10)×10=49131     B) $\left(8+10\right)\times10=49+131$(8+10)×10=49+131     C) $\left(8+10\right)\times10=49+229$(8+10)×10=49+229    D) $\left(8+10\right)\times10=49+134$(8+10)×10=49+134

 

Question 3

Complete the following number sentence: $4\times7+13=60-\editable{}$4×7+13=60

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