The 1 and Four 7’s Number Puzzle Solution

This was our challenge:

Use the numbers 7, 7, 7, 7 and 1 to create an expression that equals 100.

For this exercises you may use the addition, subtraction, multiplication and division operators along with parentheses.

The Answer

You can simplify this expression using FOIL or standard order of operations.

FOIL Method

Step 1: Multiply the “first terms” together:

Step 2: Multiply the “outside terms” together:

Step 3: Multiply the “inside terms” together:

Step 4: Multiply the “last terms” together:

Step 5: Add the products.

Standard Order of Operations

Following the standard order of operations: PEMDAS (Parenthesis, Exponents, Multiplication & Division, Addition & Subtraction moving left-to-right), begin by simplifying the expressions within the parentheses.

Step 1: Add together 7 + 1/7 by making a common denominator of 7.

Step 2: Next add 7 + 7 in the second set of parenthesis to yield 14.

Step 3: Lastly rewrite 14 as 14/1, cross-reduce and multiply the fractions.

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