Question

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Answer 1

1. Here we have to verify if the following statements are correct.

(i) $2867+986=986+2867$

⇒ $2867+986=986+2867$

⇒ $3853=3853$

∴ The commutative property is true for addition ⇒ $a+b=b+a$

(ii) $368\times215=215\times368$

⇒ $368\times215=215\times368$

⇒ $79120=79120$

∴ The commutative property is true for multiplication ⇒ $a\times b=b \times a$

(iii) $(156+273)+74=156+(273+74)$

⇒ $(156+273)+74=156+(273+74)$

⇒ $429+74 = 156+347$

⇒ $503=503$

∴ The associative property is true for addition ⇒ $a+(b+c)=(a+b)+c$

(iv) $(86\times55)\times 110 = 86\times(55\times110)$

⇒ $(86\times55)\times 110 = 86\times(55\times110)$

⇒ $4730\times 110 =86\times 6050$

⇒ $520300=520300$

∴ The associative property is true for multiplication ⇒ $a(b\times c)=(a\times b)c$

2. Here we need to simplify the following numbers using BODMAS. BODMAS is an operation in mathematics that tells us in which order a problem needs to be solved. The order of BODMAS is ⇒ Brackets, Of, Division, Multiplication, Addition and Subtraction.

(i) $39-18\div3+2\times3$

Here we need to do division first and then multiplication, then addition and finally subtraction.

⇒ $39-18\div3+2\times3$

⇒ $39-6+2\times3$

⇒ $39-6+6$

⇒ $45-6$

⇒ $39$

∴ $39-18\div3+2\times3=39$

(ii) $8+2\times 5$

Here we first need to do multiplication and then addition.

⇒ $8+2\times 5$

⇒ $8+10$

⇒ $18$

∴ $8+2\times 5=18$

(iii) $5\times 8-6\div 2$

First, we need to do division, then multiplication and finally subtraction.

⇒ $5\times 8-6\div 2$

⇒ $5\times 8-3$

⇒ $40-3$

⇒ $37$

∴$5\times 8-6\div 2=37$

(iv) $19-9\times 2$

First, we need to do multiplication and then subtraction.

⇒ $19-9\times 2$

⇒ $19-18$

⇒ $1$

∴ $19-9\times 2=1$

(v) $15\div5\times4\div 2$

First, we need to do division and then multiplication.

⇒ $15\div5\times4\div 2$

⇒ $3\times8$

⇒ $24$

∴ $15\div5\times4\div 2=24$