## Equations with Multiple Operations

**Equations with multiple operations have more than one operations within it; such as multiplication, addition, subtraction and or division **

**Let’s look at some examples …**

**Step 1: Write the equation**

47 x 28 = 47 x [ ] + 47 x 2

We need to find value of the [ ]

**Step 2: Add parenthesis at right places**

By rule first parenthesis is always around “division” operation, followed by “multiplication” operation, followed by “subtraction” and “addition”. We don’t have division operation in this equation, but, we do have “multiplication” and “addition” operations. Hence, parenthesis would be around “multiplication” operations first. The equation would become …

( 47 x 28) = (47 x [ ]) + (47 x 2)

**Step 3: Cross out all the common factors from both sides of the equation** ... in this case it is "47"

(47 x 28) = (47 x [ ])+ (47 x 2)

(28) = ([ ]) + (2)

**Step 4: Simplify the equation**

28 = [ ] + 2

**Step 5: Move over numbers to one side of the equation. Remember it changes signs**

28 – 2 = [ ]

26 = [ ] OR

[ ] = 26

**Step 6: Check if the value is correct by replacing [ ] by 26 in original equation**

(47 x 28) = (47 x [ ]) + (47 x 2)

(47 x 28) = (47 x 26 ) + (47 x 2)

1316 = 1222 + 94

1316 = 1316

Hence, the value of [ ] as 26 is correct

**Now, let's look at another example ...**

**Step 1: Write the equation**

54 x 36 = 54 x [ ] + 54 x 9

**Step 2: Add parenthesis at right places**

(54 x 36) = (54 x [ ]) + (54 x 9)

**Step 3: Cross out all common factors from both sides of the equation** .. in this case it is "54"

( x 36) = ( x [ ]) + ( x 9)

**Step 4: Simplify the equation**

36 = [ ] + 9

**Step 5: Move over numbers to one side of the equation. Remember it changes signs**

36 – 9 = [ ]

27 = [ ] OR

[ ] = 27

**step 6: Check if the value is correct**

(54 x 36)= (54 x 27) + (54 x 9)

1944 = 1458 + 486

1944 = 1944

Hence, the value of [ ] as 27 is correct

**For more detailed understanding about Equations with Multiple Operations, watch this video ...**

You can view and download Illustration related to Equations with Multiple Operations, by clicking on the image below ...

For more practice solve the following equations with multiple operations and find the value of [ ] ...

1. 82 x 41 = 82 x [ ] + 82 x 28

2. 64 x 72 = 64 x [ ] + 64 x 30

3. 93 x 35 = 93 x [ ] + 93 x 45

4. Did you find anything different about equation # 3? What was different about it?

**Still have questions??? ...**

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