Using Shapes to Represent Numbers

Open Sentences:

AlgebraAlgebra is a branch of mathematics that substitutes letters for numbers. Algebra is about finding the unknown or putting real-life variables into equations and then solving them. More is the branch of mathematics in which letters and other general symbols are used to represent numbers and quantities in formulae and equations.

We say that \( \scriptsize 15 \: + \: \boxed{?} = 20 \) is an open sentence. We can put any value in the box but usually, only one value will make the open sentence true.

\( \scriptsize 15 \: + \: \boxed{?} = 20 \) will be true if 5 goes in the box

\( \scriptsize 15 \: + \: \boxed{5} = 20 \: is \: true\)

Example 1.1.1:

Example 1.1.2:

Find the missing numbers that make the following open sentences true:

i. \( \;\;\scriptsize \boxed{?} + 7 = 14 \\ \rightarrow \scriptsize \boxed{7} + 7 = 14 \)

ii. \( \;\;\scriptsize 12 + \boxed{?} = 18 \\\rightarrow \scriptsize 12 + \boxed{6} = 18\)

iii. \(\;\; \scriptsize 14 + 7 = \boxed{?} \\ \rightarrow \scriptsize 14 + 7 = \boxed{21}\)

iv. \( \;\;\scriptsize \boxed{?} \: – \: 15 = 0 \\ \rightarrow \scriptsize \boxed{15} \: – \: 15 = 0 \)

v. \(\;\; \scriptsize 12 \: \times \: \boxed{?} = 36 \\ \rightarrow \scriptsize \scriptsize 12 \: \times \: \boxed{3} = 36\)

vi. \(\;\; \scriptsize \boxed{?} \: \times \: 5 = 40 \\ \rightarrow \scriptsize \boxed{8} \: \times \: 5 = 40 \)

vii. \( \;\; \scriptsize12 \: \div \: \boxed{?} = 3 \\ \rightarrow \scriptsize12 \; \div \: \boxed{4} = 3 \)

viii. \( \;\; \scriptsize (5 \: \times \: 8) \: – \: 5 = \boxed{?} \\ \rightarrow \scriptsize 40 \: – \: 5 = \boxed{35}\)

Remember BODMAS. We solve the values in the bracket first before we subtract.