Simplify. 13 ·(1+5) ÷13

Name: Problem 13, Chapter 1: Prealgebra and Introductory Algebra
Uploaded: 2020-06-19T17:26:58-08:00
Duration: 3 min 46 s
Channel: Jason Taylor-Pestell
Description: Simplify. 13 ·(1+5) ÷13

Key Concepts

Order of Operations

This principle, often remembered by the acronym PEMDAS (Parentheses, Exponents, Multiplication and Division (from left to right), Addition and Subtraction (from left to right)), dictates the sequence in which operations should be performed in an expression to achieve the correct result. It ensures that calculations are done consistently and accurately.

Cancellation Property

In arithmetic, when the same nonzero factor appears in both the numerator and denominator of a product, these factors can cancel each other out. This property simplifies computations by reducing the expression to a more manageable form before performing further arithmetic operations.

Simplification of Arithmetic Expressions

Simplification involves reducing an arithmetic expression to its simplest form by performing operations step-by-step and applying properties like cancellation and order of operations. This process makes it easier to compute and understand the expression while preserving its value.

Transcript

00:01 All right, so this problem is really interesting.

00:03 I'm going to show a couple of different ways to solve this problem.

00:06 I'm going to begin by doing it the longer way, just going through each of the steps, and then i'm going to show you kind of a trick that could help you in very specific situations.

00:18 Most situations are not like this.

00:20 So i have 13 times the quantity 1 plus 5 divided by 13.

00:26 And if i look at the order of operations, the most important thing is parentheses.

00:30 So i'm going to evaluate the 1 plus 5 first, which is 6.

00:37 Then i'm going to copy and paste everything that has not been used yet.

00:41 So the 13 times at the front and the divided by 13 at the end.

00:49 All right, now we're going to evaluate 13 times 6 because order of operation tells us that multiplication and division are equally important.

00:59 So both of these are equally important, but, whatever comes first in the expression.

01:06 So this just tells us they're equally important.

01:08 Right here, this came before this.

01:11 And so this has to be evaluated.

01:18 So six times 13.

01:20 I'm going to show the lattice method again.

01:22 So lattice method, you draw boxes based on the digits, two on top, one on the side, and you split them with diagonal lines, and find the answer for each digit.

01:37 So six times three and six times three, times 1.

01:40 6 times 3 is 18.

01:43 6 times 1 is 6.

01:45 So you could put a 0 here, since the answer is a 1 -digit answer instead of 2.

01:50 Then you add along the diagonals.

01:52 So this triangle is by itself.

01:54 8...