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You want to know how chapter 16 of Genesis "fits" with chapter 21.
Abraham was 86 years old when his barren wife gave him her servant-maid for the express purpose of producing children. Succeeding in becoming pregnant by Abraham, Hagar then despised Sara, which resulted in Hagar being cast out. An angel found her on the verge of death, telling her to return, and that the son to be born would be called Ishmael, and be antagonistic in nature.
Fast-forward to chapter 21 when Abraham was 100 years of age. God then fulfilled his promise to Abraham and Sarah who miraculously conceived by Abraham and bore the first child of the couple. On the feast-day of Isaac's weaning, Ishmael the 14-tear-old mocked little Isaac. That infuriated Sarah (again) who told Abraham:
"Cast out this bondwoman and her son: for the son of this bondwoman shall not be heir with my son, with Isaac." Then God told Abraham : "Let it not be grievous in thy sight, because of the lad, and because of thy bondwoman. In all that Sarah hath said unto thee, hearken unto her voice; for in Isaac shall thy seed be called. And also of the son of the bondwoman will I make a nation, because he is thy seed." Genesis 21:9-13 A.V.
This is a key point. The explanation of its significance does not arise in the Bible until the New Testament, when the apostle Paul explains it all. Galatians chapter 4 goes into the details. The previous chapter has explained how certain Jews and Gentiles are counted by God as true spiritual heirs of Abraham. Now comes the explanation of the allegory of Sarah and Hagar, and their respective sons.
Those who are spiritual sons of God are heirs of God, through Christ (putting their faith in him). From verse 22 comes the revealing of the historic account:
"For it is written, that Abraham had two sons, the one by a bondmaid, the other by a freewoman. But he who was of the bondwoman was born after the flesh; but he of the freewoman was by promise. Which things are an allegory, for these are the two covenants; the one from the mount Sinai, which gendereth to bondage, which is Hagar. For this Hagar is mount Sinai in Arabia, and answereth to Jerusalem which now is, and is in bondage with her children. But Jerusalem which is above is free, which is the mother of us all. For it is written, Rejoice, thou barren that bearest not; break forth and cry, thou that travailest not: for the desolate hath many more children than she which hath an husband. Now we, brethren, as Isaac was, are the children of promise. But as then he that was born after the flesh persecuted him that was born after the Spirit, even so it is now. Nevertheless what saith the scripture? Cast out the bondwoman and her son: for the son of the bondwoman shall not be heir with the son of the freewoman. So then, brethren, we are not children of the bondwoman, but of the free." Galatians 4:22-31 A.V.
That's how the two Genesis chapter 'fit'. The explanation in Galatians reveals the spiritual significance of those earthly, historic events regarding two women and two sons. Those with faith in Christ become heirs of Christ - "Wherefore thou are no more a servant, but a son; and if a son, then an heir of God through Christ." (Galatians 4:7). They are free in Christ as represented by Sarah and her miraculous child of promise, Isaac. They inherit spiritually, as rightful heirs. But those who are in spiritual bondage, not miraculously set free in Christ, are represented by Hagar and her son.